Hopefully I can contribute to this question by raising a little awareness about artificial sweeteners. I do try and be a health advocate, after all!
Usually these sugar free desserts are sweetened with Splenda, or its chemical name "sucralose". I'm not into ingesting chemicals, especially artificial sweeteners. The research I have done on these man made substances far outweigh any benefits (the only benefit I can think of is having something that tastes "sweet"). The only zero calorie sweetener that doesn't have any effect on blood sugar levels and is natural is Stevia, yet most places do not use this in their recipes.
Sucralose (Splenda) is a chlorinated sugar molecule, and the sweetener is actually comprised of bulking agents, dextrin and maltodextrose. These are sugars, and when used in recipes at the same proportions of sugar, they add carbohydrates which effect your blood sugar. As well as raising insulin (it might, it might not, depending on who you are--performing a simple experiment would be wise), aspartame and sucralose have been documented to contribute to excitoxicity, or the killing of brain cells (cells react to these chemicals in a way that literally "excite" them to death). Artificial sweeteners can also contribute to weight gain in many studies (I will give you these studies if you want them) by fooling your metabolism and ruining your body's ability to count calories.
It is best, at least in my opinion, when eating out, is to have fruit or your own sweetened food item with Stevia (if allowed in the parks--I don't know). Fruits are low on the glycemic index, and are bound by fiber and other nutrients that slow down the rate at which the sugar (fructose) is absorbed into the blood stream. Some higher glycemic fruits, however, off a faster spike in insulin (bananas, mangoes), yet it is still at a slower rate than sugar, and even perhaps a Splenda sweetened dessert.
I really hope I provided some help for you to go out and be healthy! If you still have to have a sugar free dessert when you go out, I don't see a problem in having it just that once. As long as you are staying healthy in every other way (exercising, sun exposure, proper sleep, meditation, etc.), your body might be strong enough to process and push out the toxins contained in artificial sweeteners.
Let me know how everything goes, and what you decide to do!
